Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -4}\frac{3 x^{2} - 15 x - 108}{5 x^{2} + 25 x + 20}$

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{0}{0}$ . Using L'Hospitial's rule and then the evaluation theorem gives: $LaTeX: \lim_{x \to -4}\frac{3 x^{2} - 15 x - 108}{5 x^{2} + 25 x + 20} = \lim_{x \to -4}\frac{6 x - 15}{10 x + 25} = \frac{6 (-4) - 15}{10 (-4) + 25} = \frac{13}{5}$